A study on a fixed-bed for Pb(ii) removal by modified alkaline lignin-sodium alginate composite hydrogel

In this work, alkaline lignin (AL) co-modified with trimercapto-s-triazine trisodium salt (TMT) and sodium alginate (SA) as a matrix were used to create a composite hydrogel for removing heavy metals, specifically divalent lead (Pb) from water. The obtained hydrogel beads were packed into a fixed bed, and then various operating conditions were explored to assess their impact on the efficiency of Pb(ii) removal. The findings indicated that the optimal removal efficiency for Pb(ii) was attained using an inflow rate of 0.159 L min−1, a hydrogel-II filling height of 40 cm, an initial Pb(ii) concentration of 10 mg L−1, and a bottom inflow direction. In the third adsorption–desorption cycle experiment, the breakthrough curve reached equilibrium after 650 min, in which equilibrium time for the initial breakthrough curve was 855 min, indicating that hydrogel-II exhibit good regeneration capability. This work serves as a foundation for practical applications in removing heavy metals from wastewater.


Introduction
3][4][5] Presently, adsorption technology is extensively utilized for treating wastewater that contains Pb(II).Compared to batch experiments of adsorption technology, xed beds are more capable of concentrating on the treatment of wastewater containing Pb(II) due to the continuous inow model. 6,7In a xed bed, when the Pb(II) solution is pumped through the bed, it is adsorbed onto its adsorbent.The performance of the adsorbent in the xed bed is typically studied using the breakthrough curves, including inuent concentration, inow rate, xed bed height, and the direction of water inow. 8Furthermore, the breakthrough time in a xed bed is also an important parameter determining its operation and dynamic response.This clearly demonstrates that a well-thought-out design of the xed bed can offer fundamental data for industrial application. 9n batch adsorption experiments, current reports mainly involve the usage of different types of modied lignin to remove Pb(II) from water. 10 However, this modied lignin is typically in the form of ne or ultrane powder, making it impractical for use in xed beds or other ow-through systems with high pressure drops.To overcome this problem, an adsorbent derived from modied lignin powder can be encapsulated in a porous carrier, such as sodium alginate (SA) hydrogel, to reduce the loss of powder adsorbent during the operation of xed beds. 11,12SA, it a natural polysaccharide derived from brown algae, has been engineered as a drug encapsulation matrix because of its safety and excellent lm-forming abilities. 13In addition to the above properties, SA can also undergo ion exchange with divalent cations (such as Ca 2+ ) to form hydrogels.This material, with its three-dimensional structure, can enhance permeability and has been widely applied in recent years for adsorption and pollutants removal. 14Currently, the main research focuses on preparing SA as hydrogels for batch adsorption experiments to remove anions (phosphate or uoride), 15,16 heavy metal oxyanions (arsenate or arsenite), 17 and dyes (Acid Black 172 or methylene blue). 18However, no studies have reported using SA-encapsulated modied lignin in xed beds for heavy metal removal.
The TMT known for its strong chelating ability with heavy metals like Pb(II), Cu(II), Cd(II), Ni(II), and Hg(II) in aqueous solutions, 19 was chosen to modify AL to enhance removal capability.This study further encapsulated TMT-modied alkaline lignin (AL) within an SA matrix to create a composite

RSC Advances
PAPER hydrogel (hydrogel-II), and then lled it into a xed bed.The study studied inuence of factors include inow rate, inow direction, initial Pb(II) concentration, and hydrogel-II lling height on Pb(II) removal.The Dose-response, Thomas, and Yoon-Nelson mathematical models were established to characterize the kinetic behavior.Moreover, the practical applications of hydrogel-II can be assessed through three consecutive adsorption-desorption cycle experiments.This research provides a theoretical basis for evaluating use potential of hydrogel-II in the real-world to remove heavy metals from water or wastewater.
Alkaline lignin (AL, black powder), trisodium trimercaptotriazine (TMT), potassium iodide, and elemental iodine, all analytical grade (Shanghai Jizhi Biochemical Technology Co., Ltd, China).Hydrochloric acid (37 wt%) and sodium hydroxide of analytical grade were obtained from Tianjin Fuyu Fine Chemical Co., Ltd.Sodium alginate (SA) and anhydrous calcium chloride, also of analytical grade, were sourced from Tianjin Fuchen Chemical Reagents Factory.The lead nitrate standard solution (1000 mg L −1 ) was used as is, without any further treatment (National Standards Testing and Certication Co., Ltd).Ultrapure water (resistivity = 18 × 10 6 U cm −1 ) was used throughout the test.

Adsorbent preparation
2.2.1 FAL preparation.The 1.0 g of AL was placed into a 500 mL beaker, accompanying by 15 mL of TMT solution and 50 mL of ultrapure water were then added.The mixture was stirred at room temperature for 120 min using a magnetic stirrer.Then the beaker was placed into a 0 °C refrigerator for 3 h, stirring manually before slowly adding 15 mL of saturated KI-I 2 solution drop by drop through a rubber bulb pipette, and letting the mixed solution stand.Aer 3 h, the beaker was removed from the refrigerator and continued to be stirred on a magnetic stirrer at room temperature for 12 h.The obtained mixture was vacuum ltered and rinsed repeatedly with ultrapure water until the ltrate was colorless.Finally, the solid substance was collected and dried under vacuum freeze-drying at −60 °C for 5 h, yielding a gray powder adsorbent (FAL).
2.2.2 Hydrogel-II preparation.The 5.0 g of SA was placed it into a 500 mL beaker, then added 250 mL of ultrapure water.Set the beaker on a magnetic stirrer and stirred at 60 °C for 5 h to dissolve the SA.The 0.4 g of FAL was added it to the beaker, stirring for another 5 h to ensure thorough mixing with the SA solution.The 16.0 g of CaCl 2 was added into a 2000 mL beaker with 500 mL of ultrapure water to prepare a CaCl 2 solution.Gradually dropped the FAL and SA mixture into CaCl 2 solution using a rubber bulb pipette to form spherical beads.Allowed the beads and CaCl 2 solution to sit for 24 h to ensure complete cross-linking of the beads.Finally, these beads were rinsed with ultrapure water until pH value of the nal rinse solution reached 6.5.The obtained beads were used as composite hydrogel adsorbent, which was referred to as hydrogel-II.This adsorbent had a particle size ranging from 0.3 to 0.5 cm.

Fixed bed construction
The xed bed was constructed through an organic glass column (length = 65 cm, diameter = 5 cm).To prevent the loss of beads with the water inow during operation, nuts with sieves were installed at both ends of the column.The inow silicone tubing applied in the xed bed was connected to the column with ttings.The beads were loaded into the glass column before establishing the connection.The Pb(II) solution inow was pumped from a supply tank located at the column's base using a peristaltic pump.The xed bed operated at room temperature, with pH value of the Pb(II) solution adjusted to 6.0 using HCl or NaOH (0.1 M).Fig. 1 presents a schematic representation of the xed bed.

Fixed bed operation experiments
During the operation of the xed bed, the studied parameters included inow rate (Q, L min −1 ), inow direction (bottom inow and top inow), initial Pb(II) concentration (C 0 , mg L −1 ), and hydrogel-II lling height (Z, cm).Breakthrough curves were generated by plotting the ratio of outlet to inlet Pb(II) concentrations (C t /C 0 , where C 0 represents the initial Pb(II) concentration and C t is the concentration at time t) against reaction time (t, min).
Fig. 1 The schematic diagram of fixed bed.
2.4.1 Effect of inow rate.The Pb(II) solution inow rates were set at 0.159, 0.255, and 0.318 L min −1 , with other parameters xed (C 0 = 10 mg L −1 , hydrogel-II lling height = 40 cm, solution pH = 6.0, and bottom inow).Based on the study of Pb(II) removal at solution pH values of 1.0, 3.0, 4.0, 5.0, and 6.0 in the batch experiment, accompanying by considering Pb(II) species at different pH levels, it was noted that adjusting solution pH to 6.0 enhanced Pb(II) removal efficiency while preventing Pb(OH) 2 precipitation. 20,21.4.2Effect of inow direction.The inow direction was varied between top and bottom, while keeping other parameters constant (solution pH = 6.0, hydrogel-II lling height = 40 cm, C 0 = 10 mg L −1 , and inow rate = 0.159 L min −1 ).
2.4.4Effect of hydrogel-II lling height.Filling heights were 20 (m = 10 g), 40 (m = 20 g), and 60 cm (m = 40 g), with other parameters held constant (solution pH = 6.0, bottom inow, C 0 = 10 mg L −1 , and inow rate = 0.159 L min −1 ).The total sampling time was 1040 min, with samples taken every 8 min from 0 to 80 min, every 40 min from 80 to 720 min, and every 80 min from 720 to 1040 min.These samples were collected and analyzed for Pb(II) concentration using ICP-OES.
2.5 Analysis of xed bed operation 2.5.1 Fixed bed data analysis.The adsorption capacity of the xed bed at breakthrough time (t b ) or saturation time (t s ), denoted as q c (mg), is usually the capacity at t s . 22The t b in the xed bed is the time required for the effluent Pb(II) concentration to reach 1.0 mg L −1 .The operation time is dened as t s when C t /C 0 = 0.90, indicating the complete loss of hydrogel-II's treatment capacity.
where Q represents the inow rate (mL min −1 ); A is the area under the breakthrough curve; t stands for breakthrough time (t b ) or saturation time (t s ) (min); C 0 is Pb(II) initial concentration (mg L −1 ); C t is Pb(II) concentration in effluent at time t (mg L −1 ).q (mg g −1 ) represents Pb(II) amount uptake by per unit mass of adsorbent in the xed bed: where m refers to hydrogel-II mass loaded in the xed bed (g).M (mg) represents the total amount of Pb(II) solution introduced into the xed bed: V eff is the effluent Pb(II) volume from the xed bed at time t s . 22Y denotes the overall removal efficiency of Pb(II): 22 To study the impact of bed height, a Bed Depth Service Time (BDST) model formulated from the simplied Bohart-Adams model was used.The BDST model was applied to investigate the impact of different lling heights on Pb(II) removal: where N 0 belongs to adsorption capacity of the xed bed (mg L −1 ); Z represents the lling height of the xed bed (cm); U 0 is the supercial velocity calculated as inow rate divided by the cross-sectional area of the column (cm min −1 ); k AB is rate constant (L mg −1 min −1 ); C b is Pb(II) concentration in effluent at breakthrough point (mg L −1 ).When dening the column service time as the duration required for the effluent Pb(II) concentration to attain 1.0 mg L −1 , the minimum theoretical depth of the xed bed necessary to keep the effluent concentration below the breakthrough level at t = 0 min is calculated.This is known as the critical height (Z 0 ) of the xed bed: 23 Moreover, the BDST model curve was transformed into a linear equation, y = ax + b, where y represents the service time (min), x is the lling height of the xed bed in centimeters, a is the slope, and b is the intercept.Here, the slope (a) = N 0 /C 0 × U 0 , and the intercept ( 24 Therefore, N 0 and k AB can be calculated from the slope and intercept of the line, respectively. 24.5.2Fixed bed breakthrough curve model.As an empirical model, the Dose-response model is widely applied to describe the kinetic properties and behavior of the xed bed columns, especially in adsorption experiments targeting heavy metals: where q 0 represents the maximum adsorption capacity (mg g −1 ), and a is the model constant.
The Thomas model is among the most extensively utilized and frequently applied theories in understanding the performance of xed bed columns. 24This model is based on Langmuir kinetics and disregards axial dispersion. 24

ln
C 0 where k Th represents the model constant (mL min −1 mg −1 ).The Yoon-Nelson model posits that the rate at which the adsorption probability for each adsorbate molecule decreases is directly proportional to both the probability of adsorbate adsorption and the occurrence of adsorbate breakthrough on the adsorbent. 26 where s represents the time (min) required for C t /C 0 to reach 50% breakthrough; k YN is the model constant (L min −1 ).
2.5.3Adsorption-desorption cycling experiment.In the cycling experiment, the xed bed operation conditions for the adsorption experiments were as follows: initial Pb(II) concentration (C 0 ) of 10 mg L −1 , solution pH of 6.0, reaction temperature of 25 °C, bottom inow, hydrogel-II lling height of 40 cm (20 g), and inow rate of 0.159 L min −1 .Sampling was conducted over a period of 1040 min, with samples collected every 8 min from 0 to 80 min, every 40 min from 80 to 720 min, and every 80 min from 720 to 1040 min.Samples were collected and analyzed for Pb(II) concentration using ICP-OES.
During desorption cycle experiment, HCl was used as the regenerating agent to remove Pb(II) from hydrogel-II surface.Other operating conditions were consistent with the adsorption experiment.Sampling was carried out over 240 min, with samples collected every 8 min and analyzed for Pb(II) concentration using ICP-OES.Aer each adsorption cycle, hydrogel-II was desorbed with HCl and washed with tap water until the inuent solution reached neutral pH.The cleaned hydrogel-II was then applied for the next adsorption experiment.The regeneration experiment was conducted for three cycles.In the cycling experiment, adsorption data were plotted using C t /C 0 to generate breakthrough curves.Desorption capacity was evaluated using individual adsorption amount, total adsorption amount, individual desorption efficiency, and cumulative desorption efficiency.
Individual desorption efficiency ¼ q 3 q 2 Â 100% Cumulative desorption efficiency ¼ where q 1 represents the individual adsorption amount (mg); q 2 is the total adsorption amount (mg); q 3 is the individual desorption amount (mg); C is Pb(II) concentration in the effluent during desorption process (mg L −1 ); V 1 denotes the volume of xed bed (L).

Scanning electron microscopy (SEM) measurement
Before measuring hydrogel-II, it is placed on a conductive silicone pad, and gold powder is sprayed onto its surface using an ion sputtering coater.During the measurement process, the electron beam acceleration voltage is set to 20.00 kV, and scanning electron microscope images of the collected samples are obtained.

Fourier transform infrared (FT-IR) spectroscopy
The sample hydrogel-II/-Pb(II) and potassium bromide (KBr) were placed in a forced air drying oven at a temperature of 80 °C for 3 h.Aerward, the sample and KBr were allowed to cool to 40 °C, removed, and placed in a vacuum bag, then cooled to room temperature (25 °C).Subsequently, a small amount of the sample was taken and placed in a mortar with KBr, ground to a powder, pressed into pellets, and the FT-IR spectrum was measured.The measurement conditions were as follows: resolution of 4 cm −1 , covering a wavelength range from 500 to 4000 cm −1 .In adsorption-desorption cycling experiment for FT-IR measurement, samples were taken for adsorption at 8, 720, and 1040 min, and for desorption at 8, 160, and 200 min.Digital photographs of the obtained samples were taken using a digital camera to observe the morphological changes of hydrogel-II beads during three consecutive regeneration cycles.

Hydrogel-II preparation
SA is a natural polysaccharide, comprising molecules linked by (1-4) b-D-mannuronic acid (M) and a-L-guluronic acid (G) connections.Due to the presence of a large amount of carboxyl groups (-COOH), SA exhibits polyanionic behavior in the aqueous solutions.Moreover, SA can undergo ion exchange reactions with divalent metal cations (such as Ca 2+ , Fe 2+ , and Sr 2+ ) through Na + in the G units. 27Due to the sugar rings of the G units being in the 1 C 4 conformation, the polymer chains can form a zigzag pattern with Ca 2+ ions, creating sack-like cavities, 27 which can be described as the egg-box model (Fig. 2).Based on the reaction mechanism described above, SA can undergo an ion exchange reaction with CaCl 2 solution, thereby preparing SA hydrogel.So this paper embedded FAL powder in SA to prepare SA-based hydrogel beads, named hydrogel-II Fig. 2 Synthetic scheme of hydrogel-II and reaction mechanism.
(Fig. 2).Furthermore, it shows that hydrogel-II surface contains some ne beads (Fig. 3a), while displays its cross-section as a porous structure (Fig. 3b), is consistent with the structure of sack-like cavities.
In prior batch adsorption studies, the primary focus was on investigating the removal capacity of hydrogel-II for Pb(II). 28The ndings suggested that the pseudo-second-order kinetics and Langmuir isotherm model provided a better t for the experimental data, indicating that the adsorption of Pb(II) onto hydrogel-II aligns with chemical adsorption and monolayer adsorption mechanisms. 28In the investigation of Pb(II) removal by hydrogel-II, the inuence of solution pH on its efficiency was also studied (Fig. 3c).The point of zero charge for hydrogel-II was determined to be 3.5. 28So it was observed that as the solution pH lower than 3.5 (1.0 and 3.0), respectively, accompanied with lower removal efficiencies (90.8 and 93.5%).At lower pH, the removal efficiency was low because the protons (H + ) can compete with the limited active sites of hydrogel-II for Pb(II), thereby reducing the removal efficiency. 29However, when the solution pH increased (4.0 to 6.0), the competition of H + with Pb(II) for active sites decreased, in which the groups in hydrogel-II undergo deprotonation, thereby enhancing the removal efficiency (96.2 to 98.8%). 29Additionally, the Pb(II) precipitation would occur when solution pH exceeds 7.2. 30,31ombining the different distribution species of Pb(II) obtained using Visual MINEQL 3.0 soware at various pH values (Fig. 3d), Pb(II) primarily exists as Pb 2+ ions in the aqueous solution when the pH ranges from 1.0 to 6.0, with a small amount present as Pb(OH) + .As described as above, when solution pH exceeds 7.0, the Pb(OH) 2 precipitation occurs.Therefore, to prevent Pb(OH) 2 precipitation from affecting the experimental results, the pH of the Pb(II) inuent solution was adjusted to 6.0.This paper further explores the removal capacity of hydrogel-II for Pb(II) by lling it in a xed bed.
3.2 Fixed bed operation experiment 3.2.1 Effect of inow rate.The inow rate is a critical parameter as it regulates the contact time between the solute and adsorbent surface.In this study, the inow rates were set at 0.159, 0.255, and 0.318 L min −1 .It was discovered that as the inow rate increased, the residual concentration of Pb(II) in the effluent from the xed bed showed a gradual increasing trend (Fig. 4a).At a lower inow rate of 0.159 L min −1 , the curve more closely resembles an S-shaped breakthrough curve, indicating a slower adsorption process.At the same time, when the inow rate increased from 0.159 to 0.318 L min −1 , the breakthrough time (t b ) of the xed bed decreased from 280 to 32 min, as well as the saturation time (t s ) decreased from 855 to 522 min (Fig. 4a and Table 1).Concurrently, as the inow rate increased, the adsorption capacity (q) at t s decreased from 42.2 to 39.4 mg g −1 , accompanied by the removal rate (Y) decreasing from 62.1% to 47.4% (Table 1).Moreover, when the inow rate increased from 0.159 to 0.318 L min −1 , the total amount of Pb(II) The results indicated that as the inow rate increases, even though both the total amount of Pb(II) entering the xed bed (M) and the effluent volume (V eff ) increase, the accelerated movement of Pb(II) through the xed bed results in insufficient residence time of Pb(II) in the column, thereby leading to a decrease in Pb(II) adsorption capacity and removal efficiency, as well as a decrease in breakthrough and penetration times. 32.2.2Effect of inow direction.The inow direction (bottom inow and top inow) in a xed bed signicantly affects the performance of hydrogel-II for Pb(II) removal. 33With bottom inow, the upward movement of water can enhance contact time between Pb(II) and hydrogel-II, leading to more efficient adsorption. 33This direction helps in preventing channeling and ensures uniform distribution of contaminants, utilizing the active sites of hydrogel-II more effectively. 33In addition, bottom inow also helps in better management of pressure drop and maintains consistent inow rates, enhancing the mass transfer rates and ensuring thorough Pb(II) uptake by hydrogel-II.Conversely, top inow can lead to quicker saturation at the upper layers, reducing overall efficiency and creating dead zones.In this work, by controlling the direction of the Pb(II) solution inow, the solution was pumped into the xed bed from the bottom (bottom inow) and the top (top inow) using a peristaltic pump.When the inow direction was from the top, the breakthrough time (t b ) of the xed bed was 120 min, and the saturation time (t s ) was 636 min (Fig. 4b and Table 1).
When the inow direction was from the bottom, the t b was determined to be 280 min, and t s was 855 min (Fig. 4b and Table 1), nding that the times were longer compared to top inow, indicating a more thorough contact between the Pb(II) solution and hydrogel-II in the xed bed.Also, when the inow direction was from the bottom, the adsorption capacity (q) of the xed bed at t s was 42.2 mg g −1 , higher than the 15.7 mg g −1 when inow direction was from the top.Furthermore, when inow direction was from the bottom, the removal efficiency (Y) of xed bed was 62.1%, the total amount of Pb(II) entering the xed bed (M) (1359 mg), and the effluent volume (V eff ) at t s (135 L) were also higher (Table 1), compared to the top inow where Y, M, and V eff were 31.1%,1011 mg, and 101 L, respectively.The results indicate that when the Pb(II) inow direction is from the bottom, it can increase the contact time between the Pb(II) solution and hydrogel-II in the xed bed, which is benecial for extending the breakthrough and penetration times, thereby improving the removal capacity for Pb(II).
3.2.3Effect of initial Pb(II) concentration.The impact of Pb(II) concentration on adsorption capacity is also a crucial factor, indicating that a given mass of adsorbent can remove only a specic quantity of Pb(II).As the initial Pb(II) concentration rose from 5 to 20 mg L −1 , there was a slight increase in the slope of the breakthrough curve from the breakthrough point to the saturation point (mass transfer zone), accompanied by a decreasing trend in both t b (breakthrough time) and t s (saturation time) (Fig. 5a and Table 2).When the initial concentration of Pb(II) was 20 mg L −1 and 10 mg L −1 , t b was 344 and 280 min, respectively, and t s was 695 and 855 min, respectively, both lower than the values at 5 mg L −1 , which were t b (410 min) and t s (927 min) (Fig. 5a and Table 2).It is commonly assumed that higher initial concentrations would lead to shorter breakthrough times; however, it is essential to recognize that the observed outcome may be inuenced by a variety of factors, including variations in mass transfer kinetics, saturation effects, and the adsorption capacity of hydrogel-II at different initial concentrations.When Pb(II) initial concentrations were 5, 10, and 20 mg L −1 , the saturated Pb(II) adsorption amounts at t s corresponded to 24.5, 42.2, and 60.5 mg g −1 .With an inow Pb(II) concentration at 5 mg L −1 , the removal rate (Y) of the xed bed for Pb(II) was 66.7%, higher than at 10 mg L −1 (62.1%) and 20 mg L −1 (54.7%).When Pb(II) initial concentrations were 5,  10, and 20 mg L −1 (Table 2), the effluent volumes (V eff ) at t s were 147, 135, and 110 L, respectively, showing a gradually decreasing trend in treatment volume as the Pb(II) concentration increased.The ndings suggested that the higher initial concentrations of Pb(II), the curve is steeper, and the solution treated is less. 34Nevertheless, at lower initial Pb(II) concentrations, the breakthrough curve extends further, indicating a greater volume of solution treated. 35Therefore, at higher initial concentrations of Pb(II), the concentration gradient increases, creating a more potent mass transfer driving force. 36his resulted in a faster migration speed of the solute within the column and a quicker saturation of the adsorption sites on hydrogel-II surface.

3.2.4
Effect of hydrogel-II lling height.The packing height of hydrogel-II in the xed bed was 20 (10), 40 (20), and 60 cm (40 g).When increasing the packing height of hydrogel-II in the xed bed, the breakthrough curve shis to the right and becomes smoother, while the slope of the curve decreases.When the packing height decreased from 60 to 20 cm, the value of t b decreased from 630 to 48 min, accompanied by t s decreasing from 1003 to 418 min (Fig. 5b and Table 2).This is because a higher packing height means a greater mass of adsorbent, leading to more available active sites for adsorption. 35,37The extension in breakthrough time results from the increased distance and duration of mass transfer zone movement at both ends of the xed bed, attributed to a higher packing layer. 35,37When the packing heights of the xed bed were 20, 40, and 60 cm, the saturated adsorption capacities (q) were 35.0, 42.2, and 42.6 mg g −1 , respectively (Table 2).Furthermore, when the packing height increased from 20 to 60 cm (Table 2), the Pb(II) effluent volume (V eff ) at t s increased from 66 to 159 L, and the value of Y for Pb(II) also increased from 52.7 to 80.1%.The results indicated that the smaller the packing height of the xed bed layer, the earlier it exhausts.However, the adsorption amounts of Pb(II) for different xed bed packing heights are similar, suggesting that increasing the packing depth of the xed bed does not have a signicant impact on the dynamic adsorption of Pb(II).The increase in packing height can also be interpreted as an increase in the mass of hydrogel-II, which provided more active sites for the removal of Pb(II).
The BDST model was utilized to delve deeper into the adsorption capabilities of hydrogel-II in the xed bed column for Pb(II).In this model, the correlation coefficient (R 2 ) is 0.9932 (Fig. 5c), indicating that the model ts the experimental data  well.The calculated adsorption capacity (N 0 ) is determined to be 1182 mg L −1 , and the k AB value is 0.003 L mg −1 min −1 .A higher N 0 value indicates faster mass transfer speed and higher adsorption efficiency of the xed bed for Pb(II). 22Hence, a larger k AB value indicates that the inuence of packing height on the adsorption capacity for Pb(II) is less signicant. 22Based on a 10% breakthrough, the minimum bed depth (Z 0 ) was calculated to be 11.6 cm, which is lower than the packing height of 20 cm, indicating a high Pb(II) removal efficiency.

Fixed bed breakthrough curve model
The adsorption behavior of hydrogel-II in a xed bed for Pb(II) is described using three models of Dose-response, Thomas, and Yoon-Nelson.The Dose-response model is an empirical model that describes the kinetics of adsorption in a xed bed.To better utilize the adsorbent and sample solution, the maximum adsorption capacity of the adsorbent is also a crucial factor to consider in the design. 25The Thomas model is used for calculating the maximum adsorption capacity of a xed bed and is one of the most commonly used models for studying breakthrough curves, assuming conformity to Langmuir isotherms and pseudo-second-order reaction kinetics. 24This model is applicable to adsorption processes where neither external nor internal diffusion limits the rate. 24The Yoon-Nelson model postulates that the likelihood of a reduction in the adsorption rate of the adsorbate on the adsorbent correlates proportionally with the probability of the adsorbate permeating through the xed bed. 26This model is not only relatively straightforward mathematically, but it also lacks stringent requirements regarding the characteristics of the adsorbate, the type of adsorbent, or the physical properties of the xed bed. 26Additionally, although the Yoon-Nelson and Thomas models have different model parameters, due to the same mathematical structure, the values of the parameters for these models obtained from tting may overlap.
Upon examining the correlation coefficients (R 2 ), a comparison revealed that the Thomas model (0.800-0.924) and the Yoon-Nelson model (0.800-0.924) exhibited more consistent values in comparison to the Dose-response model (0.564-0.947) as shown in Table 3.This suggests that the Thomas and Yoon-Nelson models provide a better t for describing the Pb(II) breakthrough curves than the Dose-response model.The adsorption amount (q 0 ) in the Thomas model (Table 3) is close to the experimental adsorption amount (q) at t s (Tables 1 and 2).Under different operating conditions (varying inow rates, inow directions, Pb(II) solution concentrations, and xed bed packing heights) (Table 3), the k TH values of the Thomas model were almost identical, and closer to 0.006 L min −1 mg −1 , indicating that Pb(II) solution volume passing through a unit mass of hydrogel-II per unit time is similar.Furthermore, increasing the inow rate, using a top inow mode, increasing the initial concentration of Pb(II), and decreasing the xed bed packing height (Table 3) led to a downward trend in s values, which might be due to the xed bed reaching adsorption saturation more quickly, indicating insufficient contact between hydrogel-II and the Pb(II) solution.

Fixed bed adsorption-desorption cycle experiments
A 0.1 mol L −1 HCl solution was used as the eluent to regenerate hydrogel-II in situ in the xed bed.Three consecutive adsorption-desorption cycle experiments were conducted.In the rst adsorption, Fig. 6a shows that the breakthrough curve of hydrogel-II reached equilibrium aer 855 min.In the rst desorption experiment, Fig. 6b indicates that the cumulative desorption rate of Pb(II) was 94%.In the second adsorption experiment, the breakthrough curve of hydrogel-II reached equilibrium aer 741 min (Fig. 6a).Moreover, in the second desorption experiment, Fig. 6b exhibits that the cumulative desorption rate decreased slightly compared to the rst desorption, at 91%.In the third adsorption experiment, Fig. 6a displays that the breakthrough curve reached equilibrium at 650 min.At the same time, the cumulative desorption rate was 90% in the third desorption experiment (Fig. 6b).The results indicate that hydrogel-II is relatively stable in the xed bed and possesses certain regeneration and recycling capabilities, thereby demonstrating its potential application prospects in the treatment of Pb(II) wastewater.

FT-IR analysis
To   ions can combine with the -COOgroups carried by hydrogel-II to form -COOH. 39 At the same time, it shows that in the rst desorption, the absorption peaks at 3426, 1610, 1420, and 812 cm −1 gradually increased as desorption time was prolonged (Fig. 7b).Moreover, the absorption peak at 1727 cm −1 also gradually intensied, consistent with the analysis during the rst adsorption cycle, due to the presence of more H + ions in solution during desorption process, leading to a more apparent increase in this peak.
In the second and third adsorption-desorption cycles (Fig. 8  and 9), similar experimental phenomena were observed as in the rst adsorption-desorption cycle.The experimental results suggest that the functional groups -OH, -COO, and the symmetric triazine ring in hydrogel-II may be the primary active sites for Pb(II) adsorption.Based on the above analysis, the mechanism of Pb(II) adsorption by hydrogel-II can be mainly summarized into the following four aspects (Fig. 10): (1) the -OH groups in hydrogel-II undergo ion exchange reactions with Pb(II), thereby forming inner-sphere complexes; 40 (2) the negatively charged -COOfunctional groups in hydrogel-II engage in electrostatic interactions with Pb(II); 41 (3) the nitrogen atoms in the symmetric triazine rings of hydrogel-II, which possess lone pairs of electrons, can form coordination bonds with Pb(II), thereby achieving Pb(II) removal; 42 and (4) according to SEM results (Fig. 3b), hydrogel-II has a porous structure.So a pore-lling effect may also exist in the process of Pb(II) removal. 43y comparing the morphology of hydrogel-II beads during the adsorption-desorption cycles (illustrations in Fig. 7a, 8a, and 9a), compared to hydrogel-II beads before Pb(II) adsorption, the beads were found to swell as adsorption time extended from 8 to 1040 min.However, in the desorption cycle experiments, the beads were slightly contracted compared to adsorption cycle (illustrations in Fig. 7b, 8b, and 9b).According to analysis, a possible reason for the above phenomena is that during adsorption process, hydrogel-II exhibits hydrophilicity, especially under the condition of an inow solution pH of 6.0, triggering swelling phenomena.However, during the desorption process, using HCl as the desorbent made the solution acidic, and the abundance of H + ions in solution causes carboxylation of the -COOgroups in hydrogel-II to form -COOH. Due to the reduced repulsion between protonated carboxyl groups, the solubility of alginate in water decreases, thereby enhancing the hydrophobicity of hydrogel-II.Therefore, during the desorption process, there was a phenomenon of  hydrogel-II particle size reduction again. 44,45Through this mechanism, the mechanical strength of hydrogel-II can be improved, thereby prolonging its service life. 44,45

Conclusion
This study explores the capacity of a xed bed to remove Pb(II) under various operating conditions and details the adsorption efficacy of hydrogel-II for Pb(II), utilizing breakthrough curves for analysis.Through three consecutive adsorption-desorption cycle experiments, the regenerative ability of hydrogel-II was explored.The results show that: (1) regeneration experiments and xed bed column experiments demonstrate that hydrogel-II can serve as an effective adsorbent for Pb(II) removal from water; (2) compared to the Dose-response model, the Thomas model and Yoon-Nelson model both better describe the breakthrough curves; (3) when inow rate of Pb(II) is 0.159 L min −1 , bottom inow, the initial Pb(II) concentration is 10 mg L −1 , and hydrogel-II packed height is 40 cm, the adsorption capacity (q 0 ) of hydrogel-II for Pb(II) was determined to be 42.2 mg g −1 ; (4) increasing the packing height of the xed bed, reducing the inow rate of the xed bed, lowering initial Pb(II) concentration, and setting the inow direction to bottom inow, the maximum adsorption capacity of Pb(II) overall shows an increasing trend, which is benecial for Pb(II) removal from water or wastewater; (5) the adsorption capacity of regenerated hydrogel-II still maintains good performance aer three adsorption-desorption cycles, indicating that hydrogel-II has potential application prospects in the treatment of Pb(II).

Fig. 3
Fig. 3 (a) SEM image of hydrogel-II surface; (b) hydrogel-II planning surface; (c) solution pH impacted on Pb(II) removal efficiency; and (d) Pb(II) species at different pH values.

Fig. 4
Fig. 4 (a) The impact of inflow rates and (b) inflow direction.

Fig. 5
Fig. 5 (a) The effect of initial Pb(II) concentration and (b) hydrogel-II filling height.(c) The BDST model.

Fig. 6
Fig. 6 Regeneration ability of hydrogel-II in a fixed bed (a) adsorption and (b) desorption.

Fig. 7
Fig. 7 FT-IR spectrum (a) first adsorption and (b) first desorption (illustrated as images of particles at different times).

Fig. 8
Fig. 8 FT-IR spectrum (a) second adsorption and (b) second desorption (illustrated as images of particles at different times).

Fig. 9
Fig. 9 FT-IR spectrum (a) third adsorption and (b) third desorption (illustrated as images of particles at different times).

Table 1
Operating parameters for fixed bed inflow rate and inflow direction

Table 2
Operating parameters for Pb(II) initial concentration and filling height

Table 3
Fitting parameters of the Dose-response, Thomas, and Yoon-Nelson models